by the group \(G\) . In the appendix of [1]}, they give an explicit way to solve this singularities. We can, therefore, associate a pair \((s_0,s_4)\)  to a triple \((X_{s_0,s_4}, C_{\pm }, \omega )\) . Of course, this association is only defined when \(s_4^{10} \ne s_0^{10}\)  and \(s_4s_0\ne 0\) , since for \(s_0=0\)  both curves \(C_+\)  and \(C_-\)  are equal. We end up with a quasi affine space \({\sf S_{op}}:= C^2\setminus \lbrace s_0s_4(s_0^{10} - s_4^{10}) = 0\rbrace \)  parametrizing the triples \((X_{s_0,s_4},C_{\pm },\omega )\) . This parametrization has an important property which we state below:
